Finite Group Databasebeta

← #27307228

Subgroups — #27307228

Order 13568.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810530C211yesmaximal, characteristic, complemented
2C2×#16810530C211yesmaximal, characteristic, complemented
3C2×#16810522C211yesmaximal, characteristic, complemented
4C2×#16810483C211yesmaximal, characteristic
5C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic53C211yesmaximal, characteristic
7#20272983C212yesmaximal, complemented
8#20272960C212yesmaximal
9#20272952C212yesmaximal
10#20272944C212yesmaximal, complemented
11C22×C22⋊Q8×C53C211yesmaximal, characteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2212yes—
14C22×C4⋊Dic53C2211yescharacteristic
15C22×C22⋊Dic53C2211yescharacteristic
16C22×C22⋊Dic53C2212yes—
17C22×C22⋊Dic53C2211yescharacteristic
18C22×C4×Dic53C2211yescharacteristic
19C22×C4×Dic53C2212yes—
20C22×C4×Dic53C2211yescharacteristic
21#16810530—24no—
22#16810530—24no—
23#16810522—24no—
24#16810483—24no—
25C4⋊C4×Dic53—24no—
26C4×C22⋊Dic53—24no—
27C2×#13133124C2211yescharacteristic
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C23×Q8×C53C2211yescharacteristic
37C24×C4×C53C2211yescharacteristic
38C2×C22⋊Q8×C53—24no—
39C2×C22⋊Q8×C53—24no—
40C2×C22⋊Q8×C53C418yescomplemented
41C22×C4⋊C4×C53C2212yes—
42C22×C4⋊C4×C53C2211yescharacteristic
43C22×C22⋊C4×C53C2212yes—
44C23×Dic53C2312yes—
45C23×Dic53C2312yes—
46C23×Dic53C2311yescharacteristic
47C23×Dic53C2311yescharacteristic
48C23×Dic53C2311yescharacteristic
49C23×Dic53C2311yescharacteristic
50C2×C4⋊Dic53—22no—
51C2×C4⋊Dic53—24no—
52C2×C4⋊Dic53—22no—
53C2×C4⋊Dic53—22no—
54C2×C4⋊Dic53—22no—
55C2×C4⋊Dic53—22no—
56C2×C4⋊Dic53—24no—
57C2×C4⋊Dic53—42no—
58C2×C4⋊Dic53D414yes—
59C2×C22⋊Dic53—22no—
60C2×C22⋊Dic53—24no—
61C2×C22⋊Dic53—22no—
62C2×C22⋊Dic53—22no—
63C2×C22⋊Dic53—24no—
64C2×C22⋊Dic53—22no—
65C2×C22⋊Dic53—22no—
66C2×C22⋊Dic53—42no—
67C2×C22⋊Dic53Q814yescomplemented
68C2×C4×Dic53—22no—
69C2×C4×Dic53—22no—
70C2×C4×Dic53—22no—
71C2×C4×Dic53—22no—
72C2×C4×Dic53—24no—
73C2×C4×Dic53—22no—
74C2×C4×Dic53—24no—
75C2×C4×Dic53—42no—
76C2×C4×Dic53D414yes—
77#13133124—24no—
78#13133124—24no—
79#13133124—24no—
80#13133124—24no—
81#13133124—24no—
82#13133124—24no—
83#13133124—22no—
84#13133124—22no—
85#13133124—24no—
86C25×C53C2311yescharacteristic
87C22×Q8×C53—22no—
88C22×Q8×C53—22no—
89C22×Q8×C53—22no—
90C22×Q8×C53—22no—
91C22×Q8×C53—22no—
92C22×Q8×C53—22no—
93C22×Q8×C53C2×C414yes—
94C23×C4×C53—22no—
95C23×C4×C53—22no—
96C23×C4×C53—22no—
97C23×C4×C53—22no—
98C23×C4×C53—22no—
99C23×C4×C53—22no—
100C23×C4×C53C2×C414yes—
101C23×C4×C53C2312yes—
102C23×C4×C53C2311yescharacteristic
103C23×C4×C53C2312yes—
104C23×C4×C53C2311yescharacteristic
105C22⋊Q8×C53—232no—
106C2×C4⋊C4×C53—24no—
107C2×C4⋊C4×C53—24no—
108C2×C4⋊C4×C53C2×C418yes—
109C2×C4⋊C4×C53C2×C414yes—
110C2×C4⋊C4×C53D414yes—
111C2×C4⋊C4×C53D414yes—
112C2×C22⋊C4×C53—24no—
113C2×C22⋊C4×C53—24no—
114C2×C22⋊C4×C53C2×C418yes—
115C24×C53—21no—
116C24×C53—21no—
117C24×C53—21no—
118C24×C53—21no—
119C24×C53—21no—
120C24×C53—21no—
121C24×C53—21no—
122C24×C53—21no—
123C24×C53—21no—
124C24×C53—21no—
125C24×C53—21no—
126C24×C53—21no—
127C24×C53C22×C412yes—
128C24×C53C2×Q812yes—
129C24×C53#4112yes—
130C24×C53C2411yescharacteristic
131C2×Q8×C53—28no—
132C2×Q8×C53—28no—
133C2×Q8×C53—28no—
134C2×Q8×C53—44no—
135C2×Q8×C53—44no—
136C2×Q8×C53—44no—
137C2×Q8×C53—44no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—28no—
155C22×C4×C53—28no—
156C22×C4×C53—28no—
157C22×C4×C53—44no—
158C22×C4×C53—44no—
159C22×C4×C53—44no—
160C22×C4×C53—44no—
161C22×C4×C53C22×C414yes—
162C22×C4×C53C22×C412yes—
163C22×C4×C53C22×C414yes—
164C22×C4×C53C22×C412yes—
165C22×C4×C53C2×D414yes—
166C22×C4×C53C2×D414yes—
167C22×C4×C53C2×D412yes—
168C22×C4×C53C2×D412yes—
169C22×C4×C53C2×D412yes—
170C22×C4×C53C2×D412yes—
171C22×C4×C53#4112yes—
172C22×C4×C53#4112yes—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—22no—
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—22no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—22no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53C2×D412yes—
209C22×Dic53C2×D414yes—
210C22×Dic53C2×D412yes—
211C22×Dic53C2×Q812yes—
212C22×Dic53C2×Q812yes—
213C22×Dic53#4112yes—
214C22×Dic53#4112yes—
215C4⋊C4×C53—216no—
216C4⋊C4×C53C22⋊C4116yescomplemented
217C22⋊C4×C53—216no—
218C22⋊Dic53—28no—
219C22⋊Dic53—28no—
220C22⋊Dic53—48no—
221C4⋊Dic53—28no—
222C4⋊Dic53—48no—
223C4⋊Dic53—44no—
224C4×Dic53—28no—
225C4×Dic53—48no—
226C4×Dic53—44no—
227C23×C53—22no—
228C23×C53—22no—
229C23×C53—22no—
230C23×C53—22no—
231C23×C53—22no—
232C23×C53—22no—
233C23×C53—22no—
234C23×C53—22no—
235C23×C53—22no—
236C23×C53—22no—
237C23×C53—22no—
238C23×C53—22no—
239C23×C53—22no—
240C23×C53—22no—
241C23×C53—22no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—22no—
245C23×C53—41no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53C4×Q814yes—
262C23×C53C23×C411yescharacteristic
263C23×C53C22×D411yescharacteristic
264C23×C53C22×D411yescharacteristic
265C23×C53C22×D411yescharacteristic
266C23×C53C22×D411yescharacteristic
267C23×C53C22×Q811yescharacteristic
268C23×C53C2×#4111yescharacteristic
269C23×C53C2×#4111yescharacteristic
270C23×C53C2×#4111yescharacteristic
271C23×C53C2×#4111yescharacteristic
272C23×C53C2×#4111yescharacteristic
273C23×C53H(5,𝔽2)11yescharacteristic
274C23×C532−1+411yescharacteristic
275C23×C532−1+411yescharacteristic
276C23×C532−1+411yescharacteristic
277Q8×C53—416no—
278C2×C4×C53—24no—
279C2×C4×C53—24no—
280C2×C4×C53—24no—
281C2×C4×C53—24no—
282C2×C4×C53—24no—
283C2×C4×C53—24no—
284C2×C4×C53—22no—
285C2×C4×C53—24no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—24no—
289C2×C4×C53—24no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—41no—
295C2×C4×C53—42no—
296C2×C4×C53—41no—
297C2×C4×C53—42no—
298C2×C4×C53—416no—
299C2×C4×C53C2×C22⋊C418yes—
300C2×C4×C53C2×C22⋊C414yes—
301C2×C4×C53C4×D414yes—
302C2×C4×C53C4×D414yes—
303C2×C4×C53#12114yes—
304C2×C4×C53#12114yes—
305C2×C4×C53#12414yes—
306C2×C4×C53#12714yes—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—24no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—24no—
320C2×Dic53—22no—
321C2×Dic53—24no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—42no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53—41no—
329C2×Dic53—41no—
330C2×Dic53—42no—
331C2×Dic53—41no—
332C2×Dic53—42no—
333C2×Dic53—41no—
334C2×Dic53—41no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—42no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53C22⋊Q814yescomplemented
349#13997—531nomaximal, Sylow
350C22×C53—24no—
351C22×C53—24no—
352C22×C53—24no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53C22×C22⋊C411yescharacteristic
366C22×C53C2×C4×D411yescharacteristic
367C22×C53C2×C4×D411yescharacteristic
368C22×C53C2×C4×Q811yescharacteristic
369C22×C53C4×#4111yescharacteristic
370C22×C53#51911yescharacteristic
371C22×C53#52011yescharacteristic
372C22×C53C2×#12111yescharacteristic
373C22×C53C2×#12111yescharacteristic
374C22×C53C2×C22⋊Q811yescharacteristic
375C22×C53#52511yescharacteristic
376C22×C53C2×#12411yescharacteristic
377C22×C53#52911yescharacteristic
378C22×C53C2×#12711yescharacteristic
379C22×C53#53311yescharacteristic
380C22×C53#53611yescharacteristic
381C22×C53#53711yescharacteristic
382C22×C53#54111yescharacteristic
383C22×C53#54211yescharacteristic
384C22×C53#54611yescharacteristic
385C22×C53#54611yescharacteristic
386C22×C53#54611yescharacteristic
387C22×C53#54711yescharacteristic
388C22×C53#54711yescharacteristic
389C22×C53#54711yescharacteristic
390C22×C53#54811yescharacteristic
391C22×C53#54811yescharacteristic
392C22×C53#54811yescharacteristic
393C22×C53D4×Q811yescharacteristic
394C22×C53D4×Q811yescharacteristic
395C22×C53D4×Q811yescharacteristic
396C22×C53#55211yescharacteristic
397C22×C53#55211yescharacteristic
398C22×C53#55411yescharacteristic
399C22×C53#55611yescharacteristic
400C4×C53—28no—
401C4×C53—42no—
402C4×C53—44no—
403C4×C53#39018yes—
404Dic53—24no—
405Dic53—42no—
406Dic53—44no—
407Dic53—42no—
408Dic53—42no—
409Dic53—82no—
410C22×C22⋊Q8D5311yescharacteristic
411C2×#391—531no—
412C2×#391—531no—
413C2×#389—531no—
414C2×#380—531no—
415C2×C4×C4⋊C4—531no—
416C2×C4×C22⋊C4—531no—
417#1445—532no—
418#1439—532no—
419#1437—532no—
420C4⋊#95—532no—
421C2×C53—44no—
422C2×C53C2×#39011yescharacteristic
423C2×C53C4×C22⋊Q811yescharacteristic
424C2×C53#232311yescharacteristic
425C2×C53#233911yescharacteristic
426C2×C53Q8×C22⋊C411yescharacteristic
427C2×C53#236011yescharacteristic
428C2×C53#236211yescharacteristic
429C2×C53#241511yescharacteristic
430C2×C53#241711yescharacteristic
431C2×C53#242711yescharacteristic
432C2×C53#242911yescharacteristic
433C2×C53#248911yescharacteristic
434C2×C53#249211yescharacteristic
435C2×C53#254011yescharacteristic
436C2×C53#254211yescharacteristic
437C23×Q8C2×D5311yescharacteristic
438C24×C4C2×D5311yescharacteristic
439C2×C22⋊Q8—24no—
440C2×C22⋊Q8—24no—
441C2×C22⋊Q8Dic5318yescomplemented
442C22×C4⋊C4—531no—
443C22×C4⋊C4—531no—
444C22×C4⋊C4—532no—
445C22×C4⋊C4C2×D5312yes—
446C22×C4⋊C4C2×D5311yescharacteristic
447C22×C22⋊C4—531no—
448C22×C22⋊C4—531no—
449C22×C22⋊C4—532no—
450C22×C22⋊C4C2×D5312yes—
451C22×C42—531no—
452C22×C42—531no—
453C22×C42—532no—
454#391—1064no—
455#391—1064no—
456#389—1064no—
457#380—1064no—
458C4×C4⋊C4—1064no—
459C4×C22⋊C4—1064no—
460C2×#95—531no—
461C2×#95—532no—
462C2×#95—532no—
463C2×#95—532no—
464C2×#95—532no—
465C2×#95—532no—
466C2×#95—532no—
467C2×#95—532no—
468C2×#95—531no—
469C53#1399711yescharacteristic, complemented, Sylow
470C25C22×D5311yescharacteristic
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8—22no—
477C22×Q8C2×Dic5314yes—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—531no—
485C23×C4—531no—
486C23×C4—532no—
487C23×C4—531no—
488C23×C4—531no—
489C23×C4—532no—
490C23×C4C2×Dic5314yes—
491C23×C4C22×D5312yes—
492C23×C4C22×D5311yescharacteristic
493C23×C4C22×D5312yes—
494C23×C4C22×D5311yescharacteristic
495C22⋊Q8—232no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—534no—
499C2×C4⋊C4—1062no—
500C2×C4⋊C4—1062no—
501C2×C4⋊C4—1064no—
502C2×C4⋊C4—1062no—
503C2×C4⋊C4—1062no—
504C2×C4⋊C4—1064no—
505C2×C4⋊C4—1062no—
506C2×C4⋊C4—2122no—
507C2×C4⋊C4C2×Dic5318yes—
508C2×C4⋊C4C2×Dic5314yes—
509C2×C4⋊C4C22⋊D5314yes—
510C2×C4⋊C4C22⋊D5314yes—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—534no—
514C2×C22⋊C4—1062no—
515C2×C22⋊C4—1062no—
516C2×C22⋊C4—1062no—
517C2×C22⋊C4—1062no—
518C2×C22⋊C4—1062no—
519C2×C22⋊C4—1064no—
520C2×C22⋊C4—1064no—
521C2×C22⋊C4—2122no—
522C2×C22⋊C4C2×Dic5318yes—
523C2×C42—534no—
524C2×C42—1062no—
525C2×C42—1062no—
526C2×C42—1064no—
527C2×C42—1062no—
528C2×C42—1062no—
529C2×C42—1064no—
530C2×C42—1062no—
531C2×C42—2122no—
532#95—1062no—
533#95—1062no—
534#95—1064no—
535#95—1064no—
536#95—1064no—
537#95—1064no—
538#95—1064no—
539#95—1064no—
540#95—1064no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24Q8×D5312yes—
554C24#1171994912yes—
555C24C22×Dic5312yes—
556C24C23×D5311yescharacteristic
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—532no—
588C22×C4—532no—
589C22×C4—532no—
590C22×C4—532no—
591C22×C4—534no—
592C22×C4—532no—
593C22×C4—532no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1062no—
605C22×C4—1061no—
606C22×C4—1062no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1061no—
613C22×C4—1061no—
614C22×C4—1062no—
615C22×C4—1061no—
616C22×C4—1061no—
617C22×C4—1061no—
618C22×C4—1062no—
619C22×C4—1061no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1062no—
625C22×C4—1062no—
626C22×C4—1062no—
627C22×C4—1062no—
628C22×C4—1062no—
629C22×C4D4×D5312yes—
630C22×C4D4×D5312yes—
631C22×C4#1171994712yes—
632C22×C4#1171994712yes—
633C22×C4C22×Dic5314yes—
634C22×C4C22×Dic5312yes—
635C22×C4C22×Dic5314yes—
636C22×C4C22×Dic5312yes—
637C22×C4C2×C22⋊D5314yes—
638C22×C4C2×C22⋊D5314yes—
639C22×C4C2×C22⋊D5312yes—
640C22×C4C2×C22⋊D5312yes—
641C4⋊C4—216no—
642C4⋊C4—1068no—
643C4⋊C4—2128no—
644C4⋊C4—2124no—
645C4⋊C4C22⋊Dic53116yescomplemented
646C22⋊C4—216no—
647C22⋊C4—1068no—
648C22⋊C4—1068no—
649C22⋊C4—2128no—
650C42—1068no—
651C42—2128no—
652C42—2124no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23Q8×Dic5314yes—
688C23C23×Dic5311yescharacteristic
689C23C2×D4×D5311yescharacteristic
690C23C2×D4×D5311yescharacteristic
691C23C22×C22⋊D5311yescharacteristic
692C23C22×C22⋊D5311yescharacteristic
693C23C2×Q8×D5311yescharacteristic
694C23#41×D5311yescharacteristic
695C23#41×D5311yescharacteristic
696C23C2×#1171994711yescharacteristic
697C23C2×#1171994711yescharacteristic
698C23C2×#1171994911yescharacteristic
699C23#1313326311yescharacteristic
700C23#1313326411yescharacteristic
701C23#1313326511yescharacteristic
702C23#1313326511yescharacteristic
703Q8—416no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—416no—
725C2×C4—534no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1064no—
733C2×C4—1064no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1064no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2122no—
749C2×C4—2122no—
750C2×C4—2122no—
751C2×C4—2121no—
752C2×C4—2121no—
753C2×C4—2121no—
754C2×C4—2121no—
755C2×C4—2122no—
756C2×C4—2121no—
757C2×C4—2121no—
758C2×C4—2121no—
759C2×C4—2121no—
760C2×C4—2122no—
761C2×C4—2121no—
762C2×C4—2121no—
763C2×C4—2121no—
764C2×C4—2121no—
765C2×C4—2122no—
766C2×C4—2122no—
767C2×C4C2×C22⋊Dic5318yes—
768C2×C4C2×C22⋊Dic5314yes—
769C2×C4D4×Dic5314yes—
770C2×C4D4×Dic5314yes—
771C2×C4#1313318814yes—
772C2×C4#1313318814yes—
773C2×C4#1313320414yes—
774C2×C4#1313321314yes—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22C22×C22⋊Dic5311yescharacteristic
791C22C2×D4×Dic5311yescharacteristic
792C22C2×D4×Dic5311yescharacteristic
793C22C2×Q8×Dic5311yescharacteristic
794C22#41×Dic5311yescharacteristic
795C22#1681110111yescharacteristic
796C22#1681110611yescharacteristic
797C22C2×#1313318811yescharacteristic
798C22C2×#1313318811yescharacteristic
799C22C22⋊Q8×D5311yescharacteristic
800C22#1681113611yescharacteristic
801C22C2×#1313320411yescharacteristic
802C22#1681115911yescharacteristic
803C22C2×#1313321311yescharacteristic
804C22#1681117511yescharacteristic
805C22#1681119611yescharacteristic
806C22#1681120311yescharacteristic
807C22#1681123311yescharacteristic
808C22#1681124611yescharacteristic
809C22#1681126111yescharacteristic
810C22#1681126111yescharacteristic
811C22#1681126411yescharacteristic
812C22#1681127211yescharacteristic
813C22#1681127211yescharacteristic
814C22#1681127511yescharacteristic
815C22#1681128311yescharacteristic
816C22#1681128411yescharacteristic
817C22#1681128411yescharacteristic
818C22#1681128611yescharacteristic
819C22Q8×C22⋊D5311yescharacteristic
820C22Q8×C22⋊D5311yescharacteristic
821C22#1681130711yescharacteristic
822C22#1681131511yescharacteristic
823C22#1681133111yescharacteristic
824C22#1681134411yescharacteristic
825C4—28no—
826C4—42no—
827C4—44no—
828C4—1064no—
829C4—4242no—
830C4—2124no—
831C4—2122no—
832C4—2122no—
833C4—2122no—
834C4#1681052618yes—
835C2—44no—
836C2C2×#1681052611yescharacteristic
837C2C22⋊Q8×Dic5311yescharacteristic
838C2#2027739911yescharacteristic
839C2#2027754511yescharacteristic
840C2Q8×C22⋊Dic5311yescharacteristic
841C2#2027772411yescharacteristic
842C2#2027774611yescharacteristic
843C2#2027814011yescharacteristic
844C2#2027816211yescharacteristic
845C2#2027828811yescharacteristic
846C2#2027831011yescharacteristic
847C2#2027905811yescharacteristic
848C2#2027909111yescharacteristic
849C2#2027965311yescharacteristic
850C2#2027966511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC22×C22⋊Q8×C53C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC22×C22⋊Q8D53
hypocenterC53#13997
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16810530C2semidirect
2. C2×#16810530C2semidirect
3. C2×#16810522C2semidirect
5. C2×C4⋊C4×Dic53C2semidirect
7. #20272983C2semidirect
10. #20272944C2semidirect
40. C2×C22⋊Q8×C53C4semidirect
67. C2×C22⋊Dic53Q8semidirect
216. C4⋊C4×C53C22⋊C4semidirect
348. C2×Dic53C22⋊Q8semidirect
441. C2×C22⋊Q8Dic53semidirect
469. C53#13997semidirect
645. C4⋊C4C22⋊Dic53semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168105302
C2×#168105222
C2×#168104832
C2×C4⋊C4×Dic532
C2×C4×C22⋊Dic532
#202729832
#202729602
#202729522
#202729442
C22×C22⋊Q8×C532
#1399753